limit x->1 (x^2-1)/(x-1) — step-by-step solution | Explain MAths

limit x->1 (x^2-1)/(x-1)

Let's evaluate the limit of

\frac{x^{2} - 1}{x - 1}

when

x \to 1

The limit of

x^{2}

is

1

when

x \to 1

The limit of

x^{2} - 1

is

0

when

x \to 1

The limit of

x - 1

is

0

when

x \to 1

For

\frac{x^{2} - 1}{x - 1}

, we encounter the indeterminate form 0/0 as

x

tends to

1

To find the limit, we factorize the numerator and the denominator:

x^{2} - 1

Factors found:

(x + 1) \cdot (x - 1)

Let's simplify:

\frac{(x + 1) \cdot (x - 1)}{x - 1}

x + 1

The limit of

x + 1

is

2

when

x \to 1

So the limit of

\frac{x^{2} - 1}{x - 1}

is

2

when

x \to 1

▷Answer: $2$